The 25-year-old Cuban, who cleared 2.38 with his first jump, has held the world record since September 1988 when he took it from Patrik Sjoberg, of Sweden.
Sotomayor has made himself clear favourite to win his first world title in Stuttgart next month. In 1991, he had to be content with second place after pulling out injured in mid-contest.
'I have been dreaming of 2.45 metres,' he said. 'If I win at the World Championships, it will have been a great year. It has already been a good year for me. . I knew the record could fall here.'
He was stopped from going to the Seoul Olympics in 1988, a few days after setting his first world record, because of a Cuban boycott.
Another world record holder, the American Mike Powell, won the long jump with the second-best leap of his career: 8.70 metres.